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### Question 1

In a certain language different symbols represent different operators as follows.

- ∩ means X = Y
- ¢ means X ≯ (not more than) Y
- @ means X ≮ (not less than) Y
- £ means X < Y
- $ means X > Y

**Statements: **F £ G; G ∩ H; H ¢ I;

**Conclusions: **

- F $ I
- G $ I

**A**

both I and II are true.

**B**

only conclusion II is true.

**C**

only conclusion I is true.

**D**

neither I nor II is true.

**Soln.**

**Ans: d**

The statements can be translated to F < G = H ≤ I. Conclusion I translates to F > I. Conclusion II translates to G > I. So we can see that neither I nor II is true.

Please remember that in such questions ≯ (not more than) is same as ≤, and ≮ (not less than) is same as ≥.

### Question 2

In a certain language different symbols represent different operators as follows.

- ¥ means X = Y
- ∧ means X ≯ (not more than) Y
- η means X ≥ Y
- Ξ means X < Y
- Γ means X > Y

**Statements: **B Ξ C; C Ξ D; D ∧ E;

**Conclusions: **

- B Γ E
- D Ξ B

**A**

both I and II are true.

**B**

only conclusion II is true.

**C**

only conclusion I is true.

**D**

neither I nor II is true.

**Soln.**

**Ans: d**

The statements can be translated to B < C < D ≤ E. Conclusion I translates to B > E. Conclusion II translates to D < B. So we can see that neither I nor II is true.

Please remember that in such questions ≯ (not more than) is same as ≤, and ≮ (not less than) is same as ≥.

### Question 3

In a certain language different symbols represent different operators as follows.

- © means X = Y
- ∑ means X ≯ (not more than) Y
- Γ means X ≮ (not less than) Y
- ∧ means X < Y
- ∀ means X > Y

**Statements: **O Γ P; P ∧ Q; Q © R;

**Conclusions: **

- P ∧ R
- Q © R

**A**

both I and II are true.

**B**

only conclusion II is true.

**C**

only conclusion I is true.

**D**

either I or II can be true.

**Soln.**

**Ans: a**

The statements can be translated to O ≥ P < Q = R. Conclusion I translates to P < R. Conclusion II translates to Q = R. So we can see that both I and II are true.

Please remember that in such questions ≯ (not more than) is same as ≤, and ≮ (not less than) is same as ≥.

### Question 4

In a certain language different symbols represent different operators as follows.

- ¢ means X = Y
- ® means X ≤ Y
- ¥ means X ≥ Y
- ∅ means X < Y
- ⊗ means X > Y

**Statements: **T ¢ U; U ∅ V; V ∅ W; W ⊗ X;

**Conclusions: **

- U ∅ X
- T ∅ X
- W ⊗ T

Which of the above conclusions is/are true?

### Question 5

In a certain language different symbols represent different operators as follows.

- £ means X = Y
- ⊗ means X ≤ Y
- ∀ means X ≥ Y
- ∏ means X < Y
- Ξ means X > Y

**Statements: **B £ C; C £ D; D Ξ E;

**Conclusions: **

- B £ E
- C Ξ E

**A**

both I and II are true.

**B**

only conclusion II is true.

**C**

only conclusion I is true.

**D**

either I or II can be true.

**Soln.**

**Ans: b**

The statements can be translated to B = C = D > E. Conclusion I translates to B = E. Conclusion II translates to C > E. So we can see that only conclusion II is true.

This Blog Post/Article "Inequalities Quiz Set 012" by Parveen (Hoven) is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.

Updated on 2019-08-18.